Drawing the graph for the equation of a circle | Maths

Starter quiz

The ______ is any line segment that joins the centre of a circle to its edge.

'radius' ✓
The value of $x^2+y^2$ when $x=3$ and $y=-4$ is ______

'25' ✓
Solve the equation $y^2=36$ .

$y=18$

$y=6$ ✓

$y=0$

$y=-6$ ✓

$y=-18$
Solve the equation $9+x^2=25$ .

$x=4$ ✓

$x=\sqrt{34}$

$x=-\sqrt{34}$

$x=-4$ ✓
Here is a right-angled triangle. The length of the side marked $r$ is ______ cm.

'10' ✓
Jun is solving the equation $x^2-2x-15=0$ . Select the correct statements.

The equation factorises to give $(x+3)(x-5)=0$ ✓

The equation factorises to give $(x-3)(x+5)=0$

The equation factorises to give $(x-3)(x-5)=0$

The solutions are $x=3$ , $x=-5$

The solutions are $x=-3$ , $x=5$

Exit quiz

Select the general form of the equation of a circle centred at the origin.

$x^2+y^2=r$

$x^2+y^2=r^2$ ✓

$x+y=r$

$x^2-y^2=r$

$x^2-y^2=r^2$
Match each equation of a circle to the radius of the circle.

$x^2+y^2=16$

⇔

4 ✓

$x^2+y^2=25$

⇔

5 ✓

$x^2+y^2-11=25$

⇔

6 ✓

$x^2+y^2=1$

⇔

1 ✓

$2x^2+y^2=9 + x^2$

⇔

3 ✓
Select the coordinates that lie on the circle with equation $x^2+y^2=100$ .

(6, 8) ✓

(10, 0) ✓

(4, 6)

(12, -2)

(8, -6) ✓
What is the equation of this circle?

$x + y = 4$

$x+y=16$

$x^2+y^2=4$

$x^2+y^2=8$

$x^2+y^2=16$ ✓
Jun draws a line and a circle on the same pair of axes to solve the equations of the line and circle simultaneously. How many possible solutions are there to the simultaneous equations?

0 ✓

1 ✓

2 ✓

3

4
Solve the simultaneous equations $x+y=4$ and $x^2+y^2=10$ .

$x=0$ and $y=4$

$x=1$ and $y=3$ ✓

$x=2$ and $y=2$

$x=3$ and $y=1$ ✓

$x=4$ and $y=0$

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

A table of values can be useful to identify coordinate pairs which satisfy the equation.
By substituting the values for x, you can calculate corresponding values for y.
If used correctly, your calculator can be a powerful tool to speed up calculations.

Common misconception

There is only value for $y$ for any given value of $x$

Pythagoras' theorem on a coordinate grid shows that there are two possible places where the $y$ -coordinate could be for any given value of $x . This is also true for the x -coordinate for any given value of y$ $

Keywords

Radius - The radius is any line segment that joins the centre of a circle to its edge.